The sides of the triangle are 5: 7: 11, and the sum of the largest and smallest sides is 80 cm.

The sides of the triangle are 5: 7: 11, and the sum of the largest and smallest sides is 80 cm. Calculate the perimeter of the triangle.

1. Let’s designate the smallest side of the triangle 5X, then the second side will be 7X, and the largest 11X. The perimeter of a triangle is equal to the sum of all its sides. Let’s write the expression and transform it:

P = 5X + 7X + 11X = 23X.

2. According to the condition of the problem, the sum of the smallest and largest sides is 80 cm. Let’s make an equation and find X:

5X + 11X = 80;

16X = 80;

X = 80/16;

X = 5.

3. Substitute the X value into the perimeter formula and calculate it:

P = 23 * 5 = 115 (cm).

Answer: the perimeter of the triangle is 115 cm.